Implied dividend and interest rate in put-call parity

T

the learner

Hi guys,

I saw the following information on the Eurostoxx option market today (expiry June 15 2018)
  • underlying: 3481,89
  • future June18: 3465
  • call 3475 BID/ASK: 41,6/42,6
  • put 3475 BID/ASK: 51,2/52,4
How can I get from the above the information about interest rate and dividend? I know in this case the options are using as underlying the future price given the future and options expire on the same date in June.
But in general this is not the case. So I think put-call parity could be used to get the information I need.
But with only ATM prices (as above), can I get this?

The formula for the implied dividend is:

d = -1/T * log(call - put + K*exp(-r*T)) / S)

where
  • K is the strike of the call and put with expiry T
  • r is the interest rate
  • S is the underlying
To solve this I still need the interest rate, so I am stuck. Any suggestion?
 
Thanks. I cannot get it from my quotes or in general? If you want to price an option and you need to pass the interest rate and the dividend yield, how do people know what values should be used exactly?
 
the learner said:
Thanks. I cannot get it from my quotes or in general?
More...
Yes, you probably can, with the caveat that implied divs are seldom accurate, even when averaged over multiple strikes.

The div-stream and rate are also embedded in the futures premium, so you really have two equations in two unknowns.

Alternatively, derive the implied rate from the total return futures (TESX instead of FESX, IRRC), which premium does not reflect the dividend stream, and then plug that rate into your formula above.
 
to get dividends: look at the spot market en compare it to futures, you need to know the interest of course for that to do the math
 
using options to try doing this makes things way too complicated since you need an estimate of vol too. Furthermore vol might be skewed.
 
Are these options on the futures? or on the cash index? If the former, there are no dividends included in the usual (Black76) futures pricing model. If the latter, use the technique in my previous post or use the futures options to derive the interest rate and then plug that into your formula.
 
Thanks for the answers.
Just to clarify, the situation I am facing is like this. I am given the bid/ask prices for 1 ATM call, 1 25D PUT and 1 25D Call.
So I want to find via put-call parity the prices of the corresponding put or call.
For example, once I have the OTM Put price I want to find the price of the same-strike Call. So I just need to find the right values for the interest rate and dividend so that, when put into the parity formula, the price I get for the same-strike Call is the same as the market price.

I was wondering if there is any practical rule of thumb I could use to achieve this.
 
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